1.3 Six Elements of ML

A defining framework for understanding concepts in the course

Recap: Machine Learning

What we saw in the previous chapter?

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A jargon cloud

How do you make sense of all the jargon?

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From jargons to jars

What are the six jars of Machine Lerarning

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Data data everywhere

What is the fuel of Machine Learning?

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Data data everywhere

How do you feed data to machines ?

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Input-1 Input-2 Input-3 Input-4 y
2.3 5.9 11.0 -10.3 0
-8.5 -1.7 -1.3 9.0 0
12.3 5.4 3.4 2.4 1
1.9 7.9 8.1 -3.3 1
-9.1 1.2 -2.1 7.8 0
3.2 -11.2 5.6 12.1 1
4.5 3.75 -1.2 -10.0 1

All data encoded as numbers

Typically high dimensional 

\mathbb{R}^n
Rn\mathbb{R}^n

@Sir Choose between 3.2 and 3.3 

Data data everywhere

How do you feed data to machines ?

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We encode all data into numbers - typically high dimension

For instance, in this course you will learn to embed image and text data as large vectors

Data entries are related - eg. given a MRI scan whether there is a tumour or not

 

Include a table that shows two/three MRI scans in first col, shows large vectors in second column, 1/0 for last column of whether there is tumour or not

 

Include a table that shows two/three reviews in first col, shows large vectors in second column, 1/0 for last column for whether review is positive or negative

 

Title the columns as x and y

All data encoded as numbers

Typically high dimensional 

\mathbb{R}^n
Rn\mathbb{R}^n
x
xx
y
yy
scans
2.3 5.9 ... 11.0 -0.3 8.9 0
-8.5 -1.7 ... -1.3 9.0 7.2 1
-0.4 6.7 ... -2.4 4.7 -7.2 0
1.6 -0.4 ... -4.6 6.4 1.9 1

Data data everywhere

How do you feed data to machines ?

(c) One Fourth Labs

We encode all data into numbers - typically high dimension

For instance, in this course you will learn to embed image and text data as large vectors

Data entries are related - eg. given a MRI scan whether there is a tumour or not

 

Include a table that shows two/three MRI scans in first col, shows large vectors in second column, 1/0 for last column of whether there is tumour or not

 

Include a table that shows two/three reviews in first col, shows large vectors in second column, 1/0 for last column for whether review is positive or negative

 

Title the columns as x and y

All data encoded as numbers

Typically high dimensional 

\mathbb{R}^n
Rn\mathbb{R}^n
x
xx
y
yy
R
2.3 5.9 ... 11.0 -0.3 8.9
-8.5 -1.7 ... -1.3 9.0 7.2
-0.4 6.7 ... -2.4 4.7 -6.2
1.6 -0.4 ... -4.6 6.4 1.9

Don't buy this MI 6 Pro, Speaker volume is very bad

Delivered as shown. Good price and fits perfect

What a phone.. A handy epic phone. MI at its best ...

​Its look stunning in pictures , but not in real.

negative

negative

positive

positive

@Sir Choose between 3.4 and 3.5 

Data data everywhere

How do you feed data to machines ?

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Input-1 Input-2 Input-3 Input-4 y
4.3 5.9 1.0 13.2 Positive
-9.5 1.7 1.3 9.2 Positive
2.3 5.4 3.8 2.9 Negative
19.1 8.9 8.2 -3.3 Positive
-9.2 11.2 -12.1 1.8 Positive
4.5 -11.2 4.6 2.1 Negative
12.2 -3.8 0.2 -1.0 Negative

All data encoded as numbers

Typically high dimensional 

\mathbb{R}^n
Rn\mathbb{R}^n

Data data everywhere

How do you feed data to machines ?

(c) One Fourth Labs

1.3 -4.3 2.1 -6.7 ... 1.5 8.9 10.1 -4.5
2.6 7.9 -0.3 8.1 ... -4.2 0.3 1.2 9.4
-5.2 -3.2 4.2 0.3 ... 3.5 8.3 -1.4 -8.7
8.5 2.1 -6.3 5.3 ... 7.2 -1.3 -4.5 11.8
2.3 -5.6 -1.2 7.8 ... 9.9 10.1 -1.1 3.5

All data encoded as numbers

Typically high dimensional 

\mathbb{R}^n
Rn\mathbb{R}^n

In this course

text

image

Data curation

Where do I get the data from?

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I am lucky

I am rich

I am smart

 +  मुंबई

 =     मुंबई

In this course

Data data everywhere

What is the fuel of Machine Learning?

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Data

Tasks

​

What do you do with this data?

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Input

Output

Hello John,

Hello John,

From product description to structured specifications

From specifications + revies to writing FAQs

From specifications + reviews + FAQs to Question Answering

From specifications + reviews + personal data to recommendations

+

+

+

Hello John,

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Tasks

What do you do with this data?

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From images identify people

Shahrukh Khan

Aamir Khan

From images identify activities

Eating

From images identify places

Gym

From posts recommend posts

Output

Input

Tasks

What do you do with this data?

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Supervised

Classification

x
xx
y
yy
3.2 5.9 ... 11.0 8.9 1
-8.5 -1.7 ... 9.0 7.2 1
-0.4 6.7 ... 4.7 -7.2 0
2.7 3.1 ... -2.1 9.7 0
3.9 7.8 ... -5.1 3.7 0
7.1 0.9 ... 1.5 -4.2 1

Tasks

What do you do with this data?

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Supervised

Regression

x
xx
-8.5 -1.7 ... 9.0 7.2 2.3 1.2 9.2 10.1
left\_x
left_xleft\_x
left\_y
left_yleft\_y
width
widthwidth
depth
depthdepth
left\_x
left_xleft\_x
left\_y
left_yleft\_y
width
widthwidth
height
heightheight
0.9 -2.1 ... -8.1 1.9 4.3 4.2 7.1 5.1
2.9 -4.5 ... -3.7 8.9 2.3 7.2 6.9 7.3

Tasks

What do you do with this data?

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Clustering

Unupervised

x
xx
3.2 5.9 ... 11.0 8.9
-8.5 -1.7 ... 9.0 7.2
-0.4 6.7 ... 4.7 -4.1
2.7 3.1 ... -2.1 9.7
3.9 7.8 ... -5.1 3.7
7.1 0.9 ... 1.5 -4.2 1

Tasks

What do you do with this data?

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Generation

Unupervised

x
xx
3.2 5.9 ... 11.0 8.9
-8.5 -1.7 ... 9.0 7.2
-0.4 6.7 ... 4.7 -4.1
2.7 3.1 ... -2.1 9.7
3.9 7.8 ... -5.1 3.7
7.1 0.9 ... 1.5 -4.2 1

Tasks

What do you do with this data?

Generation

Unupervised

x
xx
Tweets
2.3 5.9 ... 11.0 -0.3 8.9
-8.5 -1.7 ... -1.3 9.0 7.2
-0.4 6.7 ... -2.4 4.7 -6.2
1.6 -0.4 ... -4.6 6.4 1.9

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Tasks

What do you do with this data?

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\( `` \)

Supervised Learning has created 99% of economic value in AI

In this course

Classification

Regression

left\_x
left_xleft\_x
width
widthwidth
depth
depthdepth
left\_y
left_yleft\_y

Tasks

What do you do with this data?

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Data

Task

What is the mathematical formulation of a task?

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\( x \)

\( y \)

bat

car

dog

cat

Models

\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.2 \end{array} \right]\)

\( \left[\begin{array}{lcr} 0, 0, 1,0, 0 \end{array} \right]\)

\( y  = f(x) \) [true relation, unknown]

\( \hat{y}  = \hat{f}(x) \) [our approximation]

ship

\( \left[\begin{array}{lcr} 0, 1, 0, 0, 0 \end{array} \right]\)

\( \left[\begin{array}{lcr} 0, 0, 0, 0, 1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 1, 0, 0, 0, 0 \end{array} \right]\)

\( \left[\begin{array}{lcr} 0, 0, 1, 0, 0 \end{array} \right]\)

\( \left[\begin{array}{lcr} 0.1, 3.1, \dots, 1.7, 3.4\end{array} \right]\)

\( \left[\begin{array}{lcr} 0.5, 9.1,\dots, 5.1, 0.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 1.2, 4.1, \dots, 6.3, 7.4 \end{array} \right]\)

\( \left[\begin{array}{lcr} 3.2, 2.1, \dots, 3.1, 0.9 \end{array} \right]\)

Models

What are the choices for \( \hat{f} \) ?

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\( \hat{y}  = mx + c \) 

\(\hat{ y}  = ax^2 + bx + c \) 

\( y  = \sigma(wx + b) \) 

\( y  = Deep\_NN(x) \) 

\( \hat{y}  = \hat{f}(x) \) [our approximation]

\( \left [\begin{array}{lcr} 0.5\\ 0.2\\ 0.6\\ \dots\\0.3\ \end{array} \right]\)

\( \left [\begin{array}{lcr} 14.8\\ 13.3\\ 11.6\\ \dots\\6.16 \end{array} \right]\)

\( x \) 

\( y \) 

\(\hat{ y}  = ax^3 + bx^2 + cx + d \) 

\(\hat{ y}  = ax^4 + bx^3 + cx + d \) 

Data

In this course

\( y  = Deep\_CNN(x) \) ...​

\( y  = RNN(x) \)​ ...

Data is drawn from the following distribution

\vdots
⋮\vdots

\(\hat{ y}  = ax^{25} + bx^{24} + \dots + cx + d \) 

Models

Why not just use a complex model always ?

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\( \left [\begin{array}{lcr} 0.1\\ 0.2\\ 0.4\\ ....\\0.8 \end{array} \right]\)

\( \left [\begin{array}{lcr} 2.6\\ 2.4\\ 3.1\\ ....\\4.1 \end{array} \right]\)

\( x \) 

\( y \) 

\( y  = mx + c \) [true function, simple]

\(\hat{y} = ax^{100} + bx^{99} + ... + c \) 

[our approximation, very complex]

Later in this course

Bias-Variance Tradeoff

Overfitting

Regularization

Models

What are the choices for \( \hat{f} \) ?

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Data

Model

Task

Loss Function

How do we know which model is better ?

\( \left [\begin{array}{lcr} 0.00\\ 0.10\\ 0.20\\ ....\\6.40 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.24\\ 0.08\\ 0.12\\ ....\\0.36 \end{array} \right]\)

\( x \) 

\( y \) 

?

\( \hat{f_1}(x) \)

\( \left [\begin{array}{lcr} 0.25\\ 0.09\\ 0.11\\ ....\\0.36 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.32\\ 0.30\\ 0.31\\ ....\\0.22 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.08\\ 0.20\\ 0.14\\ ....\\0.15 \end{array} \right]\)

\( \hat{f_1}(x)  = a_1x^{25} + b_1x^{24} + ... + c_1x + d_1 \) 

\( \hat{f_2}(x)  = a_1x^{25} + b_1x^{24} + ... + c_1x + d_1 \) 

\( \hat{f_3}(x)  = a_1x^{25} + b_1x^{24} + ... + c_1x + d_1 \) 

\( \begin{array}{lcr} 1\\ 2\\ 3\\ ....\\n \end{array} \)

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

\( \hat{f_2}(x) \)

\( \hat{f_3}(x) \)

\( \mathscr{L}_2 = \sum_{i=1}^{n} (y_i - \hat{f}_2(x_i))^2 \) 

\( \mathscr{L}_3 = \sum_{i=1}^{n} (y_i - \hat{f}_3(x_i))^2 \) 

True Function

\( \hat{f_1}(x) \)

\( \hat{f_2}(x) \)

\( \hat{f_3}(x) \)

Loss Function

How do we know which model is better ?

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\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2  = 1.38\) 

\( \mathscr{L}_2 = \sum_{i=1}^{n} (y_i - \hat{f}_2(x_i))^2  = 2.02\) 

\( \mathscr{L}_3 = \sum_{i=1}^{n} (y_i - \hat{f}_3(x_i))^2  = 2.34 \) 

In this course

Square Error Loss

Cross Entropy Loss

KL divergence

\( \left [\begin{array}{lcr} 0.00\\ 0.10\\ 0.20\\ ....\\6.40 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.24\\ 0.08\\ 0.12\\ ....\\0.36 \end{array} \right]\)

\( x \) 

\( y \) 

\( \hat{f_1}(x) \)

\( \left [\begin{array}{lcr} 0.25\\ 0.09\\ 0.11\\ ....\\0.36 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.32\\ 0.30\\ 0.31\\ ....\\0.22 \end{array} \right]\)

\( \left [\begin{array}{lcr} 0.08\\ 0.20\\ 0.14\\ ....\\0.15 \end{array} \right]\)

\( \begin{array}{lcr} 1\\ 2\\ 3\\ ....\\n \end{array} \)

\( \hat{f_2}(x) \)

\( \hat{f_3}(x) \)

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \)

\(  = (0.24-0.25)^2  + (0.08-0.09)^2 + \newline (0.12-0.11)^2 + ... + (0.36-0.36)^2 \)

\( = 1.38 \)

Loss Function

What does a loss function look like ?

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Data

Model

Loss

Task

Learning Algorithm

How do we identify parameters of the model?

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\( \hat{f_1}(x)  = 3.5x_1^2 + 2.5x_2^{3} + 1.2x_3^{2} \) 

\( \hat{f_1}(x)  = ax_1^2 + bx_2^{3} + cx_3^{2} \) 

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

Budget
(100crore)
 		 Box Office Collection(100 crore) Action Scene times (100 mins) IMDB Rating
0.55 0.66 0.22 4.8
0.68 0.91 0.77 7,2
0.66 0.88 0.67 6.7
0.72 0.94 0.97 8.1
0.58 0.74 0.35 5.3
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots

Learning Algorithm

How do you formulate this mathematically ?

(c) One Fourth Labs

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

In practice, brute force search is infeasible

Find \(a, b, c \) such that

is minimized

\( \hat{f_1}(x)  = ax_1^2 + bx_2^{3} + cx_3^{2} \) 

Budget
(100crore)
 		 Box Office Collection(100 crore) Action Scene times (100 mins) IMDB Rating
0.55 0.66 0.22 4.8
0.68 0.91 0.77 7,2
0.66 0.88 0.67 6.7
0.72 0.94 0.97 8.1
0.58 0.74 0.35 5.3
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots

Learning Algorithm

How do you formulate this mathematically ?

(c) One Fourth Labs

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

Many optimization solvers are available

\(min_{a,b,c}\)

\( \hat{f_1}(x)  = ax_1^2 + bx_2^{3} + cx_3^{2} \) 

\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots
Budget
(100crore)
 		 Box Office Collection(100 crore) Action Scene times (100 mins) IMDB Rating
0.55 0.66 0.22 4.8
0.68 0.91 0.77 7,2
0.66 0.88 0.67 6.7
0.72 0.94 0.97 8.1
0.58 0.74 0.35 5.3

Learning Algorithm

How do you formulate this mathematically ?

(c) One Fourth Labs

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

Many optimization solvers are available

\(min_{a,b,c}\)

\( \hat{f_1}(x)  = ax_1^2 + bx_2^{3} + cx_3^{2} \) 

In this course

Gradient Descent ++

Adagrad

RMSProp

Adam

Budget
(100crore)
 		 Box Office Collection(100 crore) Action Scene times (100 mins) IMDB Rating
0.55 0.66 0.22 4.8
0.68 0.91 0.77 7,2
0.66 0.88 0.67 6.7
0.72 0.94 0.97 8.1
0.58 0.74 0.35 5.3
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots
\vdots
⋮\vdots

(c) One Fourth Labs

Learning Algorithm

How do you formulate this mathematically ?

Data

Model

Loss

Learning

Task

Evaluation

How do we compute a score for our ML model?

(c) One Fourth Labs

\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

True Labels

Predicted Labels

1

2

3

4

5

5

4

1

3

1

\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions}}{\textrm{Total number of predictions}}}
Accuracy=Number of correct predictionsTotal number of predictions\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions}}{\textrm{Total number of predictions}}}
Class Labels
Lion 1
Tiger 2
Cat 3
Giraffe 4
Dog 5
\tiny{=\frac{\textrm{4}}{\textrm{7}}}=\textrm{0.55}
=47=0.55\tiny{=\frac{\textrm{4}}{\textrm{7}}}=\textrm{0.55}

\( \left[\begin{array}{lcr} 1.9, 3.3, \dots, 4.2, 1.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)

3

5

2

5

Top - 1

Evaluation

How do we compute a score for our ML model?

(c) One Fourth Labs

\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

True Labels

Predicted Labels

1

2

3

4

5

Class Labels
Lion 1
Tiger 2
Cat 3
Giraffe 4
Dog 5

\( \left[\begin{array}{lcr} 1.9, 3.3, \dots, 4.2, 1.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)

3

5

Top - 3

\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)

\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)

\( \left[\begin{array}{lcr} 1, 2, 3\end{array} \right]\)

\( \left[\begin{array}{lcr} 4, 5, 3\end{array} \right]\)

\( \left[\begin{array}{lcr} 5, 2, 1\end{array} \right]\)

\( \left[\begin{array}{lcr} 2, 1, 4\end{array} \right]\)

\( \left[\begin{array}{lcr} 5, 4, 1\end{array} \right]\)

\tiny{=\frac{\textrm{6}}{\textrm{7}}}=\textrm{0.86}
=67=0.86\tiny{=\frac{\textrm{6}}{\textrm{7}}}=\textrm{0.86}
\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions in top-3}}{\textrm{Total number of predictions}}}
Accuracy=Number of correct predictions in top-3Total number of predictions\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions in top-3}}{\textrm{Total number of predictions}}}

Evaluation

How is this different from loss function ?

(c) One Fourth Labs

#(      )

Evaluation

Brake

/Go

__________

#(      )

Loss function

\( maximize \)

#(      )

____________________

#(      )   +   #(___)

Evaluation

Should we learn and test on the same data?

(c) One Fourth Labs

\( \left[\begin{array}{lcr} 2.1, 1.2, \dots, 5.6, 7.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 3.5, 6.6, \dots, 2.5, 6.3 \end{array} \right]\)

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)

1

2

3

4

2

\( \left[\begin{array}{lcr} 6.3, 2.6, \dots, 4.5, 3.8 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.8, 3.6, \dots, 7.5, 2.1 \end{array} \right]\)

\( \left[\begin{array}{lcr} 2.2, 1.7, \dots, 2.5, 1.8 \end{array} \right]\)

1

3

4

x
xx
y
yy
x
xx
y
yy

Training Data

Test Data

\( \mathscr{L}_1 = \sum_{i=1}^{n} (y_i - \hat{f}_1(x_i))^2 \) 

\( \hat{f_1}(x)  = ax_1^2 + bx_2^{3} + cx_3^{2} \) 

\(min_{a,b,c}\)

\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions in top-3}}{\textrm{Total number of predictions}}}
Accuracy=Number of correct predictions in top-3Total number of predictions\tiny{\textrm{Accuracy}=\frac{\textrm{Number of correct predictions in top-3}}{\textrm{Total number of predictions}}}

Evaluation

How is this different from loss function ?

(c) One Fourth Labs

Data

Model

Loss

Learning

Task

Evaluation

Putting it all together

How does all the jargon fit into these jars?

(c) One Fourth Labs

Linear Algebra

Probability

Calculus

Data

Model

Loss

Learning

Task

Evaluation

Data, democratisation, devices

Why ML is very successful?

(c) One Fourth Labs

Data

Model

Loss

Learning

Task

Evaluation

Standardised

Improvised

Democratised

Abudance

Typical ML effort

How to distribute your work through the six jars?

(c) One Fourth Labs

Your Job

Model

Loss

Learning

Evaluation

Data

Task

Connecting to the Capstone

How to distribute your work through the six jars?

(c) One Fourth Labs

Mumbai

/

/

 मुंबई \( \rightarrow \) Mumbai

 \( \sum_{i=1}^{n} (y_i - \hat{f}(x_i))^2 \)

 \( -\sum_{i=1}^{n} \log \hat{f}(x_i) \)

Accuracy

Precision/Recall

Top-k accuracy

Data

Model

Loss

Learning

Task

Evaluation

Assignment

How do you apply the six jars to a problem that you have encountered?

(c) One Fourth Labs

Explain the problem

Give link to the quiz

 

1. Formulate 3 problems from data.gov.in

 

2. In the dataturks labelled data, define tasks that you can perform and collect 10 data points for each

// Binary classification of whether there is text

// Detect text with bounding box - is accuracy easy to define here?

Ananya's copy of finalmerge

By ananya_s_b

Source: varshini7

Ananya's copy of finalmerge

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